Pentax K-1 with Canon S-type screen from focusingscreen.com

The more serious concern would be with standard K and M42 mount lenses using stop-down metering. The "cliff" at f/4 might prove problematic and unpredictable at common shooting apertures. Hand-held manual metering might end up being a good option.

This strikes me as odd, as AFAIK the EE-S screen was having a linear response against aperture when compared to standard, non-stop-down screens (such as any modern-day Pentax screens).

Reason for this is that standard screens are optimized for A-lenses with 3.5-5.6 apertures, with a fresnel lens system (explaining the concentric aspect of the screen), in order to combat small apertures and vignetting. That's what render them useless for focusing with fast lenses, as the fresnel lens actually limits the incoming rays' possible angles to something around f/2.8 (for a 50mm).

Going to the EE-S screen, you get rid of the fresnel lens, so while you get the additional rays you lose the vignetting correction.

BUT a hidden bonus (at least on my K5, I'll have to check on the K1-II) is that you regain linearity against aperture.
The f/4 'cliff' you're mentioning when using an EE-S is the real brightness loss of a f/4 lens compared to a f/2.8...